this post was submitted on 21 Oct 2024
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I don't understand this and therefore it's stupid and pointless. Fuck you math elitist assholes with your so-called "large" prime numbers spending billions of dollars that could be used to make my life better. I don't comprehend this at all and there it does not matter. The end.
If you want it to be useful for the economy and industry in order to warrant funding, I've got news for you:
The majority of modern encryption relies on prime numbers. It is currently speculated but not known, that the number of prime numbers is infinite.
Should it be proven, that there are only a finite amount of prime numbers, all encryption would become vulnerable.
Many encryption algorithms rely on the assumption that the factorizations of numbers in prime numbers has an exponential cost and not a polynomial cost (I.e. is a NP problem and not P, and we don't know if P != NP although many would bet on it). Whether there are infinite prime numbers or not is really irrelevant in the context you are mentioning, because encryption relies on factorizing finite numbers of relatively fixed sizes.
The problem is that for big numbers like n=p*q (where p and q are both prime) it's expensive to recover p and q given n.
Note that actually more modern ciphers don't rely on this (like elliptic curve crypto).